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C₃₇×#2091 #17990909

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,41,45,42,44,47,51)(40,46,48,52,49,53,50,43);(38,40,47,48,42,49,41,50)(39,43,51,46,44,52,45,53);(39,44)(45,51)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 823);